The US Department of State further complicates matters by offering an area of 45,000 sq mi agreed at the end of 1853 before the final reduction to 29,670, while wikipedia suggests that the chosen package initially came to 38,000 sq mi.

There may be a confusion among the various parallel alternative packages Gadsden was authorised to negotiate, the biggest option ($50m) including Baja California (55,360 sq mi according to wiki). So could that be where the higher number comes from?

Why State should give yet another size remains a puzzle, but its 45,000 sq mi could relate to that envisaged in the original $15m proposal for that section of the frontier before successive reductions to 38,000 or so at the signing and the eventual $10m for 29,670 sq mi.

Four numbers, four different areas of which we know one's right. But the 55,000 does seem out of line with all the others.